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arXiv · 2210.11113

PAC-Bayesian Learning of Optimization Algorithms

Michael Sucker·Peter Ochs
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Abstract

We apply the PAC-Bayes theory to the setting of learning-to-optimize. To the best of our knowledge, we present the first framework to learn optimization algorithms with provable generalization guarantees (PAC-bounds) and explicit trade-off between a high probability of convergence and a high convergence speed. Even in the limit case, where convergence is guaranteed, our learned optimization algorithms provably outperform related algorithms based on a (deterministic) worst-case analysis. Our results rely on PAC-Bayes bounds for general, unbounded loss-functions based on exponential families. By generalizing existing ideas, we reformulate the learning procedure into a one-dimensional minimization problem and study the possibility to find a global minimum, which enables the algorithmic realization of the learning procedure. As a proof-of-concept, we learn hyperparameters of standard optimization algorithms to empirically underline our theory.

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BibTeXRIS

Michael Sucker, Peter Ochs. 2022-10-20. PAC-Bayesian Learning of Optimization Algorithms. https://arxiv.org/abs/2210.11113

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